extrema concavity

If f '(x) changes from positive to negative, f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If f '(x) changes from negative to positive, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If x is a left endpoint and f '(x) is negative on the interval to the right of x, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

If x is a right endpoint and f '(x) is positive on the interval to the left of x, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

Tags

CCSS.HSF.IF.C.7

If x is a left endpoint and f '(x) is positive on the interval to the right of x, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

If x is a right endpoint and f '(x) is negative on the interval to the left of x, then f(x) has __________ at x.

• a maximum

• a minimum

• no extrema

Given the sign chart for f '(x), f(x) has ...

• a local maximum at x = -2.

• a local maximum at x = 4.

• local maxima at x = -2 and x = 4.

• no extrema.

Tags

CCSS.HSA.APR.B.3

Given the sign chart for f '(x), f(x) has ...

• a local maximum at x = -2.

• a local minimum at x = -2 and

  a local maximum at x = 4.

• a local maximum at x = -2 and

  a local minimum at x = 4.

• no extrema.

Tags

CCSS.HSA.REI.D.11

Given the sign chart for f '(x), f(x) has ...

• a local maximum at

  x = -2.

• a local maximum at

  x = 4.

• a local maximum at x = -2 and

  a local maximum at x = 4.

• no extrema.

Given the graph of f '(x), f(x) has ...

• a local min at x = -6

• a local min at x = 2

• a local min at x = 2 and

  a local max at x = -6

• local mins at x = -2, 5 and

  a local max at x = 3

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7